Statistics Questions

Question

1) A manufacturer knows that their items lifespans are normally distributed according to 

.

What proportion of the items' lifespans will be longer than 4 years? Round answer to 4 decimal places.

2) For Normally distributed data with  and .

82% of observations have values less than _____ .

Round to 1 decimal place.

3) A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 262.6-cm and a standard deviation of 2.2-cm.

A steel rod is chosen at random from all those produced by the company. What is the probability that the length of this rod is less than 269.2 cm.

Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

1)

N(3.2,0.6)

x = lifespan

to find P(x > 4) convert x to N(0,1) using z statistic: z = (x - mean)/SD = (x -3.2)/0.6.

P(x > 4) = P(z > (4 - 3.2)/0.6 = P(z > 1.33) = 1 - P(z < 1.33) = 1 - 0.9082 = 0.0918.

2)

N(117.8,2.3)

once again use z-statisitc.

For this problem, z = (x - mean)/SD = (x-117.8(/2.3

For 82%, we look up z-score corresponding to 0.82 from standard normal probability table = 0.915

so 0.915 = (x - 117.8)/2.3

x = 119.9

3) For this problem x = length N(262.6,2.2).

For this problem, z = (x - mean)/SD = (x - 262.6)/2.2

Want to find P(x < 269.2) = P(z < (269.2 - 262.6)/2.2) = P(z < 3) = 0.9987